Wash, peel and cook potatoes for about 30 minutes or until they are tender when pierced with a fork.,Drain.,Dry potatoes by shaking pan over low heat.,Mash potatoes thoroughly.,Set aside to cool completely.,Meanwhile, melt butter in a large heavy skillet on low heat.,______,Put cubes in skillet and stir until all sides are coated and browned.,Set aside.,Bring water and salt to boil in a large heavy saucepan. When potatoes are cool, whip egg in until fluffy; add a mixture of 1 teaspoon salt and pepper.,Add the cornstarch and half of the flour.,Add enough of the remaining flour to make a soft dough. Break off pieces of the dough and shape into balls about 1 inch in diameter.,Poke a bread cube into center of each ball.,Drop dumplings into the boiling water.,Cook only one layer of dumplings at a time.,Cook them 5 minutes, or until they rise to the waters surface.,Carefully remove them with a slotted spoon so they drain over the water.,Put dumplings into a warm serving dish and serve with melted butter.,Makes about 18 dumplings.